Just tossing this out there as my E30 sedan does not do this, I have only seen this on E36 cabrio's, etc.
I would guess the central locking controller and its wiring to that door gromit would be the place to start. Possibly the door switch (gets pressed when you close the door, pops out when the door opens, closing a circuit for the interior lights. Do the lights turn on as they should when you open the door?
You might be looking at taking the door panel card off and checking behind or behind the kick panel on the drivers side.
I am not sure where the E36 keeps this unit, but in E30's its in the kick panel well below the speaker.
Best thing that comes to my mind at 8AM :confused: